What causes a hesitation like thump with jolt when accelerating on 2002 Hyundai Sonata First while making a turn now occassionally also with acceleration?

The hesitation and thump you're experiencing in your 2002 Hyundai Sonata could be caused by several issues, including a failing engine mount, which can lead to excessive movement of the engine during acceleration or turns. Additionally, problems with the transmission, such as low fluid levels or a slipping clutch, could also result in a jolt or hesitation. Worn-out suspension components or issues with the drivetrain, such as CV joints, might contribute to the symptoms as well. It's advisable to have a qualified mechanic diagnose the issue for an accurate assessment.